Arbitrary superpositions of \(|a_n\rangle _1\)  and \(|b_n\rangle _1\)  cannot be copied with an arbitrarily high fidelity (quality), as states the so called no-cloning theorem [1]}, [2]}, [3]}, [4]}.
The theorem assumes, however, that it is perfectly possible in principle to do so for a particular (preferred) orthonormal basis.
This explains our choice in Eq.(REF ).
Here, we intend to find the best replicator allowed by nature (by quantum mechanics, in this case), with the goal of verifying whether it does consume a maximal amount of work.
In other words, we look for a model for \(U_n\) , trying to fulfill the perfect cloning as allowed in principle for the eigenenergies of the lambda systems.
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